An important consideration in generalised least squares problems is that the dimension of the covariance matrix V is the dimension of the data set and is large when the data set is large. Also, the problem solution can be well determined in cases where V is illconditioned or singular. Here aspects of a class of methods which factorize the design matrix while leaving V invariant, and which can b...

In this paper we study the synthesis of space-time optimal systolic arrays for the Cholesky Factorization (CF). First, we discuss previous allocation methods and their application to CF. Second, stemming from a new allocation method we derive a space-time optimal array, with nearest neighbor connections, that requires 3N + Θ(1) time steps and N2/8 + Θ(N) processors, where N is the size of the p...

In a fuzzy classifier with ellipsoidal regions, each cluster is approximated by a center and a covariance matrix, and the membership function is calculated using the inverse of the covariance matrix. Thus when the number of training data is small, the covariance matrix becomes singular and the generalization ability is degraded. In this paper, during the symmetric Cholesky factorization of the ...

This is a survey paper on algorithms that have been developed during the last 25 years for the explicit computation of the structure of an associative algebra of finite dimension over either a finite field or an algebraic number field. This constructive approach was initiated in 1985 by Friedl and Rónyai and has since been developed by Cohen, de Graaf, Eberly, Giesbrecht, Ivanyos, Küronya and W...

A modified Cholesky factorization algorithm introduced originally by Gill and Murray and refined by Gill, Murray and Wright, is used extensively in optimization algorithms. Since its introduction in 1990, a different modified Cholesky factorization of Schnabel and Eskow has also gained widespread usage. Compared with the Gill-Murray-Wright algorithm, the Schnabel-Eskow algorithm has a smaller a...

In our previous work, we have developed the backward feature selection method based on class regions approximated by ellipsoids. In this paper, we accelerate feature selection by the forward selection search, the symmetric Cholesky factorization, and deletion of duplicated calculations between consecutive factorizations. The feature selection for two data sets shows that our method is faster th...

In this article, we propose a computationally efficient approach to estimate (large) p-dimensional covariance matrices of ordered (or longitudinal) data based on an independent sample of size n. To do this, we construct the estimator based on a k-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerabl...

A generalized q-Pilbert matrix from [2] is further generalized, introducing one additional parameter. Explicit formulæ are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger’s celebrated algorithm. However, the necessary identities ...

Matrix factorization (or often called decomposition) is a frequently used kernel in a large number of applications ranging from linear solvers to data clustering and machine learning. The central contribution of this paper is a thorough performance study of four popular matrix factorization techniques, namely, LU, Cholesky, QR, and SVD on the STI Cell broadband engine. The paper explores algori...